Pre-Algebra Examples

$(4 z^{3} + 12 z + 6) \div 2 z$

Step 1

Rewrite the division as a fraction.

$\frac{4 z^{3} + 12 z + 6}{2 z}$

Step 2

Cancel the common factor of $4 z^{3} + 12 z + 6$ and $2$ .

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Step 2.1

Factor $2$ out of $4 z^{3}$ .

$\frac{2 (2 z^{3}) + 12 z + 6}{2 z}$

Step 2.2

Factor $2$ out of $12 z$ .

$\frac{2 (2 z^{3}) + 2 (6 z) + 6}{2 z}$

Step 2.3

Factor $2$ out of $2 (2 z^{3}) + 2 (6 z)$ .

$\frac{2 (2 z^{3} + 6 z) + 6}{2 z}$

Step 2.4

Factor $2$ out of $6$ .

$\frac{2 (2 z^{3} + 6 z) + 2 \cdot 3}{2 z}$

Step 2.5

Factor $2$ out of $2 (2 z^{3} + 6 z) + 2 (3)$ .

$\frac{2 (2 z^{3} + 6 z + 3)}{2 z}$

Step 2.6

Cancel the common factors.

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Step 2.6.1

Factor $2$ out of $2 z$ .

$\frac{2 (2 z^{3} + 6 z + 3)}{2 (z)}$

Step 2.6.2

Cancel the common factor.

$\frac{2 (2 z^{3} + 6 z + 3)}{2 z}$

Step 2.6.3

Rewrite the expression.

$\frac{2 z^{3} + 6 z + 3}{z}$

Step 3

Split the fraction $\frac{2 z^{3} + 6 z + 3}{z}$ into two fractions.

$\frac{2 z^{3} + 6 z}{z} + \frac{3}{z}$

Step 4

Split the fraction $\frac{2 z^{3} + 6 z}{z}$ into two fractions.

$\frac{2 z^{3}}{z} + \frac{6 z}{z} + \frac{3}{z}$

Step 5

Cancel the common factor of $z^{3}$ and $z$ .

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Step 5.1

Factor $z$ out of $2 z^{3}$ .

$\frac{z (2 z^{2})}{z} + \frac{6 z}{z} + \frac{3}{z}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Raise $z$ to the power of $1$ .

$\frac{z (2 z^{2})}{z^{1}} + \frac{6 z}{z} + \frac{3}{z}$

Step 5.2.2

Factor $z$ out of $z^{1}$ .

$\frac{z (2 z^{2})}{z \cdot 1} + \frac{6 z}{z} + \frac{3}{z}$

Step 5.2.3

Cancel the common factor.

$\frac{z (2 z^{2})}{z \cdot 1} + \frac{6 z}{z} + \frac{3}{z}$

Step 5.2.4

Rewrite the expression.

$\frac{2 z^{2}}{1} + \frac{6 z}{z} + \frac{3}{z}$

Step 5.2.5

Divide $2 z^{2}$ by $1$ .

$2 z^{2} + \frac{6 z}{z} + \frac{3}{z}$

Step 6

Cancel the common factor of $z$ .

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Step 6.1

Cancel the common factor.

$2 z^{2} + \frac{6 z}{z} + \frac{3}{z}$

Step 6.2

Divide $6$ by $1$ .

$2 z^{2} + 6 + \frac{3}{z}$